Complex parts formed via additive manufacturing and similar techniques often incorporate united cellular lattice structures for reducing overall weight, increasing strength, and improving other properties of the parts. The united cellular lattice structures are modeled by merging together a large number of lattice cells. Each individual lattice cell includes a number of face surfaces that adjoin face surfaces of adjacent lattice cells. These adjoining face surfaces (i.e., “shared face surfaces”) are not needed and thus are often removed when the lattice cells are merged together. Creating and removing the shared face surfaces is time intensive and significantly slows or delays computation of the united lattice cellular structures. It is also difficult to determine if all of the adjoining face surfaces have been removed properly, resulting in some adjoining face surfaces accidentally not being removed. This may result in computational or rendering errors or even additive manufacturing errors. For example, additive manufacturing material may be deposited incorrectly resulting in structural weaknesses, inadequate seals, weight imbalances, and other imperfections.